Relation between topology and heat currents in multilevel absorption machines

Abstract

The steady state heat currents of continuous absorption machines can be decomposed into thermodynamically consistent contributions, each of them associated with a circuit in the graph representing the master equation of the thermal device. We employ this tool to study the functioning of absorption refrigerators and heat transformers with an increasing number of active levels. Interestingly, such an analysis is independent of the particular physical implementation (classical or quantum) of the device. We provide new insights into the understanding of scaling up thermal devices concerning both the performance and the magnitude of the heat currents. Indeed, it is shown that the performance of a multilevel machine is smaller or equal than the corresponding to the largest circuit contribution. Besides, the magnitude of the heat currents is well-described by a purely topological parameter which in general increases with the connectivity of the graph. Therefore, we conclude that for a fixed number of levels, the best of all different constructions of absorption machines is the one whose associated graph is as connected as possible, with the condition that the performance of all the contributing circuits is equal.The analysis of the thermodynamic quantities can be realized at different levels of description [24]. From a macroscopic point of view, where the relevant quantities are the bath temperatures and the physical (total) heat currents, to a microscopic description that considers in addition the device structure. This latter perspective is more and more relevant as the advance of the experimental techniques allows for the design and the manipulation of the device. A prominent tool for this microscopic analysis is graph theory, where the stochastic master equation for the populations is represented by a graph. Schnakenberg theory [25] is a popular approach that gives a decomposition of the total entropy production based on a set of fundamental circuits in the graph. Basically, Schnakenberg applies Kirchhoff's current laws to reduce the number of terms appearing in the entropy production, which may be highly beneficial for optimization procedures. It has been used for example in linear irreversible thermodynamics [26] and in the study of steady-state fluctuation theorems [27,28]. This method does not intend to associate an entropy production with each circuit. In particular, the attempt to interpret individually each term in the decomposition may lead to apparent negative entropy productions, although this problem can be avoided by a convenient choice of the fundamental circuits [29][30][31]. However, it has been shown that the diagnosis of the machine performance greatly benefits from considering the thermodynamic analysis of not only the fundamental but all the possible circuits in the graph [32][33][34]. A convenient approach is then Hill theory [35]. Schnakenberg and Hill theory assign the same affinity to each circuit, but the latter considers all the possible circuits and leads to thermodynamically consistent ent...

Effects of Noise-Induced Coherence on the Performance of Quantum Absorption Refrigerators

“…is composed of three terms: the system Hamiltonian [19,20,21,22,23,24]). In all these studies, a specific model of quantum absorption refrigerator is investigated which cannot be mapped to the models considered by us.…”

“…[9]). 23 and f 31 = f 32 . The structure of the equations guarantees the necessary condition ρ 12 = ρ * 21 .…”

Classical emulation of quantum-coherent thermal machines

“…Note that this holds for any periodically-driven model and not just for those with a cyclic transition pattern. Similarly, all heat-driven (or 'absorption') thermal machines with non-degenerate energy spectra are incoherent in their energy basis and thus, classically emulable in the weak coupling limit [56]. Furthermore, the equivalence between multi-stroke and continuous heat devices in the small action limit [30] provides a means to generalize our "classical simulability" argument to reciprocating quantum thermodynamic cycles.…”

“…The graph-theoretic expression (32) for the circuit currents of the classical emulator can also prove useful in the performance optimization of our quantum-coherent thermal machines S [56]. For instance, from the bracketed factor we see that the asymmetry in the stationary rates associated with opposite cycles is crucial in increasing the energy-conversion rate.…”

“…Such emulator is defined by a graph G with three circuits: the original circuit C N , a two-edge circuit C 2 -with vertices j w and j w +1-corresponding to power dissipation into the hot bath, and a N-edge circuit C N , where the work edge is replaced by the new hot edge, related to a heat leak from the hot to the cold bath. The heat currents and power of these circuits can be obtained by following the techniques explained in [55] and [56]. The total heat currents are then the sum of the following three thermodynamically consistent contributionṡ…”